Pietersen (186) and Cook (122) both moved level on 22 hundreds with three all-time greats in Wally Hammond, Geoff Boycott and Colin Cowdrey as England's most prolific Test centurions.
Their stand of 206 was broken when Cook edged an off-break from Ravichandran Ashwin to slip, but Pietersen dug in to take England to a lead of 86.
Monty Panesar (five for 61) then took his match haul to 10 wickets with the prize scalps of Virender Sehwag and Sachin Tendulkar for the second time in the match.
Graeme Swann also repeated his new party trick to see off Cheteshwar Pujara, for the second time in five balls after the number three had previously batted almost 18 hours in this series without being dismissed, as India barely struggled back in front on a hapless 117 for seven.
Pietersen has drawn contrasting superlatives during an especially eventful year in his mercurial career - and there will be many more of the complimentary variety after an innings in which, Cook apart, he played on a different level to all around him.
His latest virtuoso carried England to 413 all out, despite the best efforts of Pragyan Ojha (five for 143) in conditions so conducive to his left-arm spin and a late clatter of four wickets for seven runs in 13 balls.
Pietersen's first Test hundred since his summer of discontent and subsequent 'reintegration' came at a pivotal point as the tourists seek to overturn a 27-year pattern by winning a series in India.
Cook's second successive hundred following his rearguard 176 in last week's defeat at Ahmedabad was a very significant contribution too.
Out on his own already with his fourth century in his first four Tests as captain after his two while standing in for Andrew Strauss in Bangladesh two-and-a-half years ago, he reached three figures today with a cover-drive off Harbhajan Singh for his 11th four.
Pietersen operated at a quicker tempo throughout to give England telling impetus and rubber-stamp his return to the fold after his well-chronicled contract wrangles and disagreements with management and senior players.
Five minutes after Cook completed his century, Pietersen did likewise, from only 127 balls, with an impudent reverse-sweep just wide of slip off Harbhajan for his 15th four.
By his often exuberant standards, a controlled celebration followed, with England still in arrears.
When Cook finally departed, Pietersen jogged 30 yards down the wicket and past the stumps to lend his personal acknowledgement as the captain made his way off the pitch.
Controversially, new batsman Jonny Bairstow could not quite survive the morning, poking a catch to silly-point off Ojha in the final over of the session.
The young Yorkshireman walked straight off, apparently oblivious either to the fact Gautam Gambhir had completed the sharp catch via the bottom of his helmet grille - or that such effect should have meant dead ball.
The lunch break provided England with the chance to make representations on the matter to the umpires, and India, but to no avail, and it was Samit Patel who emerged with Pietersen to start the afternoon.
Pietersen treated Ojha in particular with near disdain, hitting him for three of his four sixes, the first of two slog-sweeps to go to 150 and draw England level and another crashed almost lazily over extra-cover.
Patel provided manful support, watchful mostly on the back foot, until he pushed forward instead to Ojha and edged sharp turn and bounce to gully.
Pietersen was to fall short of a fourth Test double-century, a trademark flat-bat shot at Ojha resulting in a tame edge behind, and Matt Prior was run out after a mix-up over an aborted single to kick-start England's late collapse to spin.
Their lead was perhaps not as significant as it should have been.
But it looked ample by stumps after Sehwag had been caught at gully, Pujara and Yuvraj Singh at short-leg, Virat Kohli off a Swann full-toss at mid-off, captain Mahendra Singh Dhoni at slip and finally Ashwin at cover.
For good measure, in a near binary scorecard apart from opener Gambhir's unbeaten 53, Tendulkar went for just eight again, lbw to an arm ball this time, in what may well prove a forgettable final Test innings on his home ground.